{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f8ba3161",
   "metadata": {},
   "source": [
    "# Interp 8: Adding auxillary variables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6535c1f2",
   "metadata": {},
   "source": [
    "When we do a regression task, it might be good to include auxillary input variables, even though they might be dependent on other variables. For example, to regress $m(m_0, v, c)=m_0/\\sqrt{1-(v/c)^2}$, it is desirable to include the dimensionaless varabile $\\beta = v/c$ as a separate input variable. If we also know this is a task in relativity, we may also include $\\gamma=1/\\sqrt{1-(v/c)^2}$ because $\\gamma$ appears frequently in relativity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "3b818211",
   "metadata": {},
   "outputs": [],
   "source": [
    "from kan.MultKAN import MultKAN\n",
    "from sympy import *\n",
    "from kan.utils import create_dataset, augment_input\n",
    "import torch\n",
    "\n",
    "seed = 3\n",
    "torch.manual_seed(seed)\n",
    "torch.set_default_dtype(torch.float64)\n",
    "torch.use_deterministic_algorithms(True)\n",
    "\n",
    "input_variables = m0, v, c = symbols('m0 v c')\n",
    "\n",
    "# define auxillary variables\n",
    "beta = v/c\n",
    "gamma = 1/sqrt(1-beta**2)\n",
    "\n",
    "aux_vars = (beta, gamma)\n",
    "\n",
    "f = lambda x: x[:,[0]]/torch.sqrt(1-x[:,[1]]**2/x[:,[2]]**2)\n",
    "dataset = create_dataset(f, n_var=3, ranges=[[0,1],[0,0.9],[1.1,2]])\n",
    "\n",
    "# add auxillary variables\n",
    "dataset = augment_input(input_variables, aux_vars, dataset)\n",
    "input_variables += aux_vars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "c386c245",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "checkpoint directory created: ./model\n",
      "saving model version 0.0\n"
     ]
    }
   ],
   "source": [
    "model = MultKAN(width=[5,[0,1]], mult_arity=2, grid=3, k=3, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "59c8b0d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 14 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model(dataset['train_input'])\n",
    "model.plot(in_vars=input_variables, out_vars=[m0/sqrt(1-v**2/c**2)], scale=1.0, varscale=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "2951afef",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 5.96e-04 | test_loss: 9.16e-04 | reg: 4.06e+00 | : 100%|█| 50/50 [00:11<00:00,  4.42it"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "model.fit(dataset, steps=50, lamb=1e-5, lamb_coef=1.0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "71656f49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 14 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(in_vars=input_variables, out_vars=[m0/sqrt(1-v**2/c**2)], scale=1.0, varscale=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "b2b17686",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.2\n"
     ]
    }
   ],
   "source": [
    "model = model.prune()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "d2e07789",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 3.57e-06 | test_loss: 1.85e-05 | reg: 3.40e+00 | : 100%|█| 100/100 [00:17<00:00,  5.87"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.3\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "model.fit(dataset, steps=100, lamb=0e-3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a84176d4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6e8cfa58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fixing (0,0,0) with x, r2=0.999999999868798, c=1\n",
      "fixing (0,0,1) with 0\n",
      "fixing (0,1,0) with 0\n",
      "fixing (0,1,1) with 0\n",
      "fixing (0,2,0) with 0\n",
      "fixing (0,2,1) with 0\n",
      "fixing (0,3,0) with 0\n",
      "fixing (0,3,1) with 0\n",
      "fixing (0,4,0) with 0\n",
      "fixing (0,4,1) with x, r2=0.9999997733953018, c=1\n",
      "saving model version 0.4\n"
     ]
    }
   ],
   "source": [
    "model.auto_symbolic()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a230671a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.0 \\cdot \\left(9.0376427738903 \\cdot 10^{-5} - \\frac{0.852508537795552}{\\sqrt{1 - \\frac{v^{2}}{c^{2}}}}\\right) \\left(- 1.17312547362696 m_{0} - 1.12252012796077 \\cdot 10^{-7}\\right)$"
      ],
      "text/plain": [
       "1.0*(9.0376427738903e-5 - 0.852508537795552/sqrt(1 - v**2/c**2))*(-1.17312547362696*m0 - 1.12252012796077e-7)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sf = model.symbolic_formula(var=input_variables)[0][0]\n",
    "sf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c8414225",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{m_{0}}{\\sqrt{1 - \\frac{v^{2}}{c^{2}}}}$"
      ],
      "text/plain": [
       "m0/sqrt(1 - v**2/c**2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from kan.utils import ex_round\n",
    "\n",
    "nsimplify(ex_round(ex_round(ex_round(sf,6),3),3))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
